In this paper develops and applies a new geometrical model of a fixed-focus solar concentrator (CSFF) in Cartesian coordinates, which incorporates the thermal model of a cavity receiver to determine the design parameters of CSFF needed to satisfy the thermal energy demand of a 3-kWe Stirling engine. The numerical validation of the proposed model is made from experimental results reported concentrator WGA500 and receiver system PROMES CNRS. The numerical results providing the dimensions of CSFF, which similarly to the parabolic dish, the highest concentration was obtained with edge angle 45° but with the difference that the receiver operates with in fixed position and receptor efficiency of 88%. The proposed model and methodology can be used for sizing CSFF coupled receptors open cavity according to the heat and temperature requirements of the application.